Question

b) z= log₃ 2 · log₄ 3 · log₅ 4 · log₆ 5 ?

Answer 1

$\displaystyle z=\log_32\cdot \log_43\cdot\log_54\cdot\log_65\\\\ z= \frac{\ln2}{\ln3} \cdot \frac{\ln3}{\ln4} \cdot \frac{\ln4}{\ln5} \cdot \frac{\ln5}{\ln6} = \frac{\ln2\ln3\ln4\ln5}{\ln3\ln4\ln5\ln6} = \frac{\ln2}{\ln6}=\boxed{\log_62}$